Vague Mereology and Borderline Connections

The summit of Mt Everest is determinately part of it; parts of the Khumbu Glacier are determinately not. In between are a range of candidate parts whose mereological status with respect to Everest is unsettled. Among the various accounts of vagueness, supervaluationism has received a great deal of attention. But very little attention has been paid to supervaluational theories of mereological relations themselves, and formal mereologies set within supervaluational logics are largely unexplored. In this paper, we provide two formal semantics for a vague mereology. We start with a simple supervaluational system using overlap as a primitive under a global consequence relation, but argue that it is unsatisfactory. We then develop a richer framework based on the idea of borderline connections, and expand it to a modal semantics of precisifications with a determinacy operator under a local consequence relation. We then prove a range of results, including the equivalence between borderline connection and indeterminate overlap, the vagueness of minimal and maximal fusions, and the distinction between mereological and compositional vagueness. The framework is intended to be compatible with a range of philosophical interpretations, including epistemic, semantic, and ontic views of vagueness.